51 research outputs found

    Nonlocal symmetries of integrable two-field divergent evolutionary systems

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    Nonlocal symmetries for exactly integrable two-field evolutionary systems of the third order have been computed. Differentiation of the nonlocal symmetries with respect to spatial variable gives a few nonevolutionary systems for each evolutionary system. Zero curvature representations for some new nonevolution systems are presented

    Properties of the Scalar Universal Equations

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    The variational properties of the scalar so--called ``Universal'' equations are reviewed and generalised. In particular, we note that contrary to earlier claims, each member of the Euler hierarchy may have an explicit field dependence. The Euler hierarchy itself is given a new interpretation in terms of the formal complex of variational calculus, and is shown to be related to the algebra of distinguished symmetries of the first source form.Comment: 15 pages, LaTeX articl

    Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations

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    The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible complex transformations can be used to obtain invertible real transformations that map a system of nonlinear partial differential equations into a system of linear partial differential equation. Explicit invariant criteria are given that provide procedures for writing down the solutions of the linearized equations. A few non-trivial examples are mentioned.Comment: This paper along with its first part ODE-I were combined in a single research paper "Linearizability criteria for systems of two second-order differential equations by complex methods" which has been published in Nonlinear Dynamics. Due to citations of both parts I and II these are not replaced with the above published articl

    Thiazolidinediones enhance vascular endothelial growth factor expression and induce cell growth inhibition in non-small-cell lung cancer cells

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    <p>Abstract</p> <p>Background</p> <p>It is known that thiazolidinediones are involved in regulating the expression of various genes, including the vascular endothelial growth factor (VEGF) gene via peroxisome proliferator-activated receptor γ (PPARγ); VEGF is a prognostic biomarker for non-small-cell lung cancer (NSCLC).</p> <p>Methods</p> <p>In this study, we investigated the effects of troglitazone and ciglitazone on the mRNA expression of VEGF and its receptors in human NSCLC cell lines, RERF-LC-AI, SK-MES-1, PC-14, and A549. These mRNA expressions were evaluated by quantitative real-time reverse transcription-polymerase chain reaction (RT-PCR) analysis. We also studied the effect of Je-11, a VEGF inhibitor, on the growth of these cells.</p> <p>Results</p> <p>In NSCLC cells, thiazolidinediones increased the mRNA expression of VEGF and neuropilin-1, but not that of other receptors such as fms-like tyrosine kinase and kinase insert domain receptor-1. Furthermore, the PPARγ antagonist GW9662 completely reversed this thiazolidinedione-induced increase in VEGF expression. Furthermore, the addition of VEGF inhibitors into the culture medium resulted in the reversal of thiazolidinedione-induced growth inhibition.</p> <p>Conclusions</p> <p>Our results indicated that thiazolidinediones enhance VEGF and neuropilin-1 expression and induce the inhibition of cell growth. We propose the existence of a pathway for arresting cell growth that involves the interaction of thiazolidinedione-induced VEGF and neuropilin-1 in NSCLC.</p

    Mitochondrial Variability as a Source of Extrinsic Cellular Noise

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    We present a study investigating the role of mitochondrial variability in generating noise in eukaryotic cells. Noise in cellular physiology plays an important role in many fundamental cellular processes, including transcription, translation, stem cell differentiation and response to medication, but the specific random influences that affect these processes have yet to be clearly elucidated. Here we present a mechanism by which variability in mitochondrial volume and functionality, along with cell cycle dynamics, is linked to variability in transcription rate and hence has a profound effect on downstream cellular processes. Our model mechanism is supported by an appreciable volume of recent experimental evidence, and we present the results of several new experiments with which our model is also consistent. We find that noise due to mitochondrial variability can sometimes dominate over other extrinsic noise sources (such as cell cycle asynchronicity) and can significantly affect large-scale observable properties such as cell cycle length and gene expression levels. We also explore two recent regulatory network-based models for stem cell differentiation, and find that extrinsic noise in transcription rate causes appreciable variability in the behaviour of these model systems. These results suggest that mitochondrial and transcriptional variability may be an important mechanism influencing a large variety of cellular processes and properties

    Innate Immune Responses of Drosophila melanogaster Are Altered by Spaceflight

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    Alterations and impairment of immune responses in humans present a health risk for space exploration missions. The molecular mechanisms underpinning innate immune defense can be confounded by the complexity of the acquired immune system of humans. Drosophila (fruit fly) innate immunity is simpler, and shares many similarities with human innate immunity at the level of molecular and genetic pathways. The goals of this study were to elucidate fundamental immune processes in Drosophila affected by spaceflight and to measure host-pathogen responses post-flight. Five containers, each containing ten female and five male fruit flies, were housed and bred on the space shuttle (average orbit altitude of 330.35 km) for 12 days and 18.5 hours. A new generation of flies was reared in microgravity. In larvae, the immune system was examined by analyzing plasmatocyte number and activity in culture. In adults, the induced immune responses were analyzed by bacterial clearance and quantitative real-time polymerase chain reaction (qPCR) of selected genes following infection with E. coli. The RNA levels of relevant immune pathway genes were determined in both larvae and adults by microarray analysis. The ability of larval plasmatocytes to phagocytose E. coli in culture was attenuated following spaceflight, and in parallel, the expression of genes involved in cell maturation was downregulated. In addition, the level of constitutive expression of pattern recognition receptors and opsonins that specifically recognize bacteria, and of lysozymes, antimicrobial peptide (AMP) pathway and immune stress genes, hallmarks of humoral immunity, were also reduced in larvae. In adults, the efficiency of bacterial clearance measured in vivo following a systemic infection with E. coli post-flight, remained robust. We show that spaceflight altered both cellular and humoral immune responses in Drosophila and that the disruption occurs at multiple interacting pathways

    Targeting cancer metabolism: a therapeutic window opens

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    Genetic events in cancer activate signalling pathways that alter cell metabolism. Clinical evidence has linked cell metabolism with cancer outcomes. Together, these observations have raised interest in targeting metabolic enzymes for cancer therapy, but they have also raised concerns that these therapies would have unacceptable effects on normal cells. However, some of the first cancer therapies that were developed target the specific metabolic needs of cancer cells and remain effective agents in the clinic today. Research into how changes in cell metabolism promote tumour growth has accelerated in recent years. This has refocused efforts to target metabolic dependencies of cancer cells as a selective anticancer strategy.Burroughs Wellcome FundSmith Family FoundationStarr Cancer ConsortiumDamon Runyon Cancer Research FoundationNational Institutes of Health (U.S.

    Symmetry-based algorithms to relate partial differential equations

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    An algorithm is presented to linearize nonlinear partial differential equations by non-invertible mappings. The algorithm depends on finding nonlocal symmetries of the given equations which are realized as appropriate local symmetries of a related auxiliary system. Examples include the Hopf-Cole transformation and the linearizations of a nonlinear heat conduction equation, a nonlinear telegraph equation, and the Thomas equations. 1

    A Canonical Transformation for Equation of the Form φ x

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